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Block #2,558,909

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/10/2018, 4:09:04 PM Β· Difficulty 10.9917 Β· 4,274,772 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
67fc088d4e6b2847e1966b5c018fabf1bc8ba0ca2794f1582a75ec3bc27b3663
View on Chainz β†—

Height

#2,558,909

Difficulty

10.991732

Transactions

2

Size

425 B

Version

2

Bits

0afde226

Nonce

1,274,656,858

Timestamp

3/10/2018, 4:09:04 PM

Confirmations

4,274,772

Mined by

⛏️ P2SHAHVhMvH9LKPZzHwp14HAgUM8V5pmWQpBzR

Merkle Root

32139d406c3cee5956f6c9ee770f389687554d5b7cb5b4de387c6a63c5ad6877
Transactions (2)
Coinbasea2fc950d96956a…be408484908dad
1 in β†’ 1 out8.2700 XPM110 B
AHVhMvH9…pmWQpBzR
a62ed85e2c561c…8211fd5d4cd046
1 in β†’ 2 out2.0742 XPM225 B
AWocb5y7…77rQQqbCAUxYadQb…inUR4QFa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.771 Γ— 10⁹³(94-digit number)
57712987144478819391…68348572752000451199
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.771 Γ— 10⁹³(94-digit number)
57712987144478819391…68348572752000451199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.771 Γ— 10⁹³(94-digit number)
57712987144478819391…68348572752000451201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.154 Γ— 10⁹⁴(95-digit number)
11542597428895763878…36697145504000902399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.154 Γ— 10⁹⁴(95-digit number)
11542597428895763878…36697145504000902401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.308 Γ— 10⁹⁴(95-digit number)
23085194857791527756…73394291008001804799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.308 Γ— 10⁹⁴(95-digit number)
23085194857791527756…73394291008001804801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.617 Γ— 10⁹⁴(95-digit number)
46170389715583055513…46788582016003609599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.617 Γ— 10⁹⁴(95-digit number)
46170389715583055513…46788582016003609601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.234 Γ— 10⁹⁴(95-digit number)
92340779431166111026…93577164032007219199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.234 Γ— 10⁹⁴(95-digit number)
92340779431166111026…93577164032007219201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.846 Γ— 10⁹⁡(96-digit number)
18468155886233222205…87154328064014438399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,913,667 XPMΒ·at block #6,833,680 Β· updates every 60s
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